Q. 2TB - Calculus

Question

Setting up and solving a word problem involving arc length: Calvin wants to hang some Christmas lights along the edge of the front side of his garage roof. The edge of the front side of the roof of his garage is a curve in the shape of a downwards-pointing parabola extending 3 feet above the ceiling of the garage and 12 feet across. How long a string of Christmas lights does Calvin need?

Step-by-Step Solution

Answer

a

Step 1: Arc length formula

The arc length of a curve \(y = f(x)\) from \(x = a\) to \(x = b\) is \(L = \int_a^b \sqrt{1+[f'(x)]^2}\,dx\).

Step 2: Apply to the problem

Model the roof edge as a curve, set up the integral using the given dimensions, and evaluate to find the length of Christmas lights needed.